Question

Simplest form of (1 - cos2 A) (1 + cot? A) is​

Answer 1

Answer:1

Step-by-step explanation:

1 - cos^2A = sin^2A

1 + cot^2A = cosec^2A

(Sin^2A)(cosec^2A)

= sin^2A × 1/sin^2A = 1

Answer 2

The simplest form of the given expression $(1-cos^2A)(1+cosec^2A)$ is 1

Step-by-step explanation:

Given expression is $(1-cos^2A)(1+cot^2A)$

To find the simplest form of the give expression :

First simplify  the given expression from that we have as below

• $(1-cos^2A)(1+cot^2A)$
• $=(sin^2A)(cosec^2A)$   ( by using the identities $(1-cos^2A)=sin^2A$ and $(1+cot^2A)=cosec^2A$ )
• $=sin^2A\times (\frac{1}{sin^2A})$ ( by using the identity $cosec^2A=\frac{1}{sin^2A}$ )
• $=\frac{sin^2A}{sin^2A}$
• $=1$ ( simplifing the terms )
• Therefore we get $(1-cos^2A)(1+cosec^2A)=1$

The simplest form of the given expression $(1-cos^2A)(1+cosec^2A)$ is 1